A bstract We consider the form factor bootstrap approach of integrable field theories to derive matrix elements composite branch-point twist fields associated with symmetry resolved entanglement entropies. The equations are determined in an intuitive way and their solution is presented for massive Ising theory genuinely interacting sinh-Gordon model, both possessing a ℤ 2 symmetry. solutions carefully cross-checked by performing various limits application ∆-theorem. issue resolution discrete...

We generalise the form factor bootstrap approach to integrable field theories with U(1) symmetry derive matrix elements of composite branch-point twist fields associated resolved entanglement entropies. The equations are solved for free massive Dirac and complex boson theories, which simplest symmetry. present exact complete solution bootstrap, including vacuum expectation values factors involving any type arbitrarily number particles. non-trivial solutions carefully cross-checked by...

In this paper we continue the programme initiated in Part I, that is study of entanglement measures sine-Gordon model. both parts, have focussed on one specific technique, well-known connection between branch point twist field correlators and 1+1D integrable quantum theory. Our papers apply technique for first time to a non-diagonal theory with an involved particle spectrum, II focus different measure, symmetry resolved entanglement, develop its associated description, exploiting underlying...

We discuss the nonequilibrium time evolution of phase field in sine-Gordon model using two very different approaches: truncated Wigner approximation and conformal space approach. demonstrate that approaches agree for a period covering first few oscillations, thereby giving solid theoretical prediction framework model, which is thought to describe dynamics bosonic condensates quasi-one-dimensional traps coupled via Josephson tunneling term. conclude, however, recently observed phase-locking...

A bstract In this paper, we apply the form factor bootstrap approach to branch point twist fields in q -state Potts model for ≤ 3. For = 3 is an integrable interacting quantum field theory with internal discrete ℤ symmetry and therefore provides ideal starting investigation of resolved entanglement entropies. However, more generally, standard Rényi entropies are also accessible through programme. our work present solutions both composite (or resolved) cases, equations solved two particles...

We investigate the non-equilibrium dynamics of symmetry-resolved R\'enyi entropies in a one-dimensional gas non-interacting spinless fermions by means quantum generalised hydrodynamics, which recently allowed to obtain very accurate results for total entanglement inhomogeneous quench settings. Although our discussion is valid any setting accessible with we focus on case initially prepared bipartite fashion and subsequently let evolve unitarily hopping Hamiltonian. For this system,...

We study inhomogeneous quantum quenches in the attractive regime of sine-Gordon model. In our protocol, system is prepared an initial state finite volume by coupling topological charge density operator to a Gaussian external field. After switching off field, subsequent time evolution governed homogeneous Hamiltonian. Varying either interaction strength model or amplitude source interesting transition observed expectation value soliton density. This affects both profile and its can be...

The authors study the full counting statistics of particle number in one-dimensional interacting Bose and Fermi gases which have been quenched far from equilibrium. They consider time evolution Lieb-Liniger Gaudin-Yang models, could be relevant to experiments on ultracold gases.

We consider the problem of determining initial state integrable quantum field theory quenches in terms post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods treat quenches. construct and examine an infinite integral equation hierarchy based on form factor bootstrap, proposed earlier as set conditions deter- mining overlaps. Using mass interaction Sinh-Gordon concrete example, we present theoretical arguments that has squeezed coherent expected for...

We present a numerical computation of overlaps in mass quenches sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence method, we use novel running coupling definition which has general applicability free boson TCSA. The results are used to confirm validity previously proposed analytical Ansatz for initial state sinh-Gordon quench.

Spreading on networks is influenced by a number of factors, including different parts the inter-event time distribution (IETD), topology network and non-stationarity. In order to understand role these factors we study SI model temporal with aggregated topologies IETDs. Based analytic calculations numerical simulations, show that if stationary bursty process governed power-law IETD, spreading can be slowed down or accelerated as compared Poisson process; speed determined short behaviour,...

Topological excitations or defects such as solitons are ubiquitous throughout physics, supporting numerous interesting phenomena like zero-energy modes with exotic statistics and fractionalized charges. In this paper, we study objects through the lens of symmetry-resolved entanglement entropy. Specifically, compute charge-resolved entropy for a single interval in low-lying states Su-Schrieffer-Heeger model presence topological defects. Using combination exact asymptotic analytical...

Truncated Conformal Space Approach (TCSA) is a highly efficient method to compute spectra, operator matrix elements and time evolution in quantum field theories defined as relevant perturbations of 1+1-dimensional conformal theories. However, similarly other exact diagonalisation methods, TCSA ridden with the "curse dimensionality": dimension Hilbert space increases exponentially (square root the) truncation level, limiting its precision by available memory resources. Here we describe an...

A bstract We study the Rényi entanglement entropies along massless renormalisation group flow that connects tricritical and critical Ising field theories. Similarly to massive integrable theories, we derive a set of bootstrap equations, from which can analytically calculate twist form factors in recursive way. Additionally, also obtain them as non-trivial ‘roaming limit’ sinh-Gordon theory. Then are obtained expansions terms these branch point fields. find factor expansion entropy organises...

A bstract We study homogeneous quenches in integrable quantum field theory where the initial state contains zero-momentum particles. demonstrate that two-particle pair amplitude necessarily has a singularity at threshold. Albeit explicit discussion is carried out for special (integrable) states, we argue inevitably present and generic feature of involving creation zero momentum also identify Ising model across critical point, compute it perturbatively phase sine-Gordon which are potentially...

The quantum sine-Gordon model is the simplest massive interacting integrable field theory whose two-particle scattering matrix generally non-diagonal. As such, it a that has been extensively studied, especially in context of bootstrap program. In this paper we compute low particle-number form factors special local known as branch point twist field, correlation functions are building blocks for measures entanglement. We consider attractive regime where possesses particle spectrum consisting...

We study the massless flows described by staircase model introduced Al.B. Zamolodchikov through analytic continuation of sinh-Gordon S-matrix, focusing on renormalisation group flow from tricritical to critical Ising model. show that properly defined roaming limits certain form factors are identical order and disorder operators for flow. As a by-product, we also construct semi-local field in model, which can be associated with twist ultraviolet limiting free bosonic theory.

A bstract We study Euler scale hydrodynamics of massless integrable quantum field theories interpolating between two non-trivial renormalisation group fixed points after inhomogeneous quenches. Using a partitioning protocol with left and right initial thermal states the recently developed framework generalised hydrodynamics, we focus on current density profiles for energy momentum as function ξ = x/t , where both x t are sent to infinity. Studying first few members n D flows carry out...

A bstract The effect of unstable quasiparticles in the out-of-equilibrium dynamics certain integrable systems has been subject several recent studies. In this paper we focus on stationary value entanglement entropy density, its growth rate, and related functions, after a quantum quench. We consider quenches, each which is characterised by corresponding squeezed coherent state. quench action approach, state amplitudes K ( θ ) become input data that fully characterise large-time state, thus...

Topological excitations or defects such as solitons are ubiquitous throughout physics, supporting numerous interesting phenomena like zero energy modes with exotic statistics and fractionalized charges. In this paper, we study objects through the lens of symmetry-resolved entanglement entropy. Specifically, compute charge-resolved entropy for a single interval in low-lying states Su-Schrieffer-Heeger model presence topological defects. Using combination exact asymptotic analytical...

We study the effects of integrability breaking on relaxation dynamics (double) sine-Gordon model. Compared to previous studies, we apply an alternative viewpoint motivated by open-system physics separating phase field into homogeneous and inhomogeneous parts, describing a quantum pendulum (subsystem) interacting phononic bath (environment). To in model, perform quenches using mini-superspace-based truncated Hamiltonian approach developed recently simulate real-time evolution various...

The statistics of fluctuations on large regions space encodes universal properties many-body systems. At equilibrium, it is described by thermodynamics. However, away from equilibrium such as after quantum quenches, the fundamental principles are more nebulous. In particular, although exact results have been conjectured in integrable models, a correct understanding physics largely missing. this letter, we explain these principles, taking example number particles lying interval...

We study the R\'enyi entanglement entropies along massless renormalisation group flow that connects tricritical and critical Ising field theories. Similarly to massive integrable theories, we derive a set of bootstrap equations, from which can analytically calculate twist form factors in recursive way. Additionally, also obtain them as non-trivial roaming limit sinh-Gordon theory. Then are obtained expansions terms these branch point fields. find factor expansion entropy organises two...